Introduction to optimal control, adaptive control and reinforcement learning

2013 ◽  
pp. 1-8
Keyword(s):  
Optimal Control ◽  
Adaptive Control ◽  
Reinforcement Learning

scholarly journals Convergence results for an averaged LQR problem with applications to reinforcement learning

2021 ◽  
Author(s):  
Andrea Pesare ◽  
Michele Palladino ◽  
Maurizio Falcone
Keyword(s):  
Optimal Control ◽  
Reinforcement Learning ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Current System ◽  
Numerical Test ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Lqr Problem ◽  
Quadratic Optimal Control

AbstractIn this paper, we will deal with a linear quadratic optimal control problem with unknown dynamics. As a modeling assumption, we will suppose that the knowledge that an agent has on the current system is represented by a probability distribution $$\pi $$ π on the space of matrices. Furthermore, we will assume that such a probability measure is opportunely updated to take into account the increased experience that the agent obtains while exploring the environment, approximating with increasing accuracy the underlying dynamics. Under these assumptions, we will show that the optimal control obtained by solving the “average” linear quadratic optimal control problem with respect to a certain $$\pi $$ π converges to the optimal control driven related to the linear quadratic optimal control problem governed by the actual, underlying dynamics. This approach is closely related to model-based reinforcement learning algorithms where prior and posterior probability distributions describing the knowledge on the uncertain system are recursively updated. In the last section, we will show a numerical test that confirms the theoretical results.

Hierarchical Terrain-Aware Control for Quadrupedal Locomotion by Combining Deep Reinforcement Learning and Optimal Control

2021 ◽  
Author(s):  
Qingfeng Yao ◽  
Jilong Wang ◽  
Donglin Wang ◽  
Shuyu Yang ◽  
Hongyin Zhang ◽  
...  
Keyword(s):  
Optimal Control ◽  
Reinforcement Learning ◽  
Quadrupedal Locomotion

scholarly journals Online Optimal Control of Robotic Systems with Single Critic NN-Based Reinforcement Learning

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Xiaoyi Long ◽  
Zheng He ◽  
Zhongyuan Wang
Keyword(s):  
Optimal Control ◽  
Reinforcement Learning ◽  
Tracking Control ◽  
Learning Algorithm ◽  
Tracking Error ◽  
Adaptive Dynamic Programming ◽  
Robotic Systems ◽  
Control Synthesis ◽  
Optimal Tracking ◽  
Optimal Tracking Control

This paper suggests an online solution for the optimal tracking control of robotic systems based on a single critic neural network (NN)-based reinforcement learning (RL) method. To this end, we rewrite the robotic system model as a state-space form, which will facilitate the realization of optimal tracking control synthesis. To maintain the tracking response, a steady-state control is designed, and then an adaptive optimal tracking control is used to ensure that the tracking error can achieve convergence in an optimal sense. To solve the obtained optimal control via the framework of adaptive dynamic programming (ADP), the command trajectory to be tracked and the modified tracking Hamilton-Jacobi-Bellman (HJB) are all formulated. An online RL algorithm is the developed to address the HJB equation using a critic NN with online learning algorithm. Simulation results are given to verify the effectiveness of the proposed method.

scholarly journals Prefrontal solution to the bias-variance tradeoff during reinforcement learning

2020 ◽  
Author(s):  
Dongjae Kim ◽  
Jaeseung Jeong ◽  
Sang Wan Lee
Keyword(s):  
Adaptive Control ◽  
Reinforcement Learning ◽  
Prediction Error ◽  
Brain Regions ◽  
Decision Task ◽  
Prediction Errors ◽  
Model Based ◽  
Model Free ◽  
Bias Variance ◽  
The Brain

AbstractThe goal of learning is to maximize future rewards by minimizing prediction errors. Evidence have shown that the brain achieves this by combining model-based and model-free learning. However, the prediction error minimization is challenged by a bias-variance tradeoff, which imposes constraints on each strategy’s performance. We provide new theoretical insight into how this tradeoff can be resolved through the adaptive control of model-based and model-free learning. The theory predicts the baseline correction for prediction error reduces the lower bound of the bias–variance error by factoring out irreducible noise. Using a Markov decision task with context changes, we showed behavioral evidence of adaptive control. Model-based behavioral analyses show that the prediction error baseline signals context changes to improve adaptability. Critically, the neural results support this view, demonstrating multiplexed representations of prediction error baseline within the ventrolateral and ventromedial prefrontal cortex, key brain regions known to guide model-based and model-free learning.One sentence summaryA theoretical, behavioral, computational, and neural account of how the brain resolves the bias-variance tradeoff during reinforcement learning is described.

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